Multipaction

Multipaction is an effect that occurs with RF fields, usually in a vacuum or
low pressure condition. Essentially it results from an ion moving back and forth
(in response to an RF field) and knocking other electrons off the sides when
it hits. If the transit time of the electron is nicely synchronized with the
RF field, then just as it hits, the field is right to pull the new electrons
towards the other side, and a cascading avalanche can result (if the electron
emission coefficient (greek lower case delta) is >1). The table below gives
values for clean, outgassed surfaces. Bear in mind that without special cleaning,
surfaces can have a delta as high as 4.

Secondary Electron Coefficient

Metal

d (electrons per incident electron)

Electron Energy at deltamax
(eV)

Electron Energy for delta=1
(eV)

Al

1.9

220

35

Au

1.1

330

160

Cu

1.3

240

100

Fe

1.3

350

120

Mo

1.3

360

120

Ni

1.3

460

160

W

1.45

700

200

As the number of electrons bouncing back and forth grows, the current can increase
to the point where a hot spot forms on the cavity wall, increasing outgassing,
melting the wall, evaporating material, and all manner of "bad things."

A bunch of math will result in a handy equation, often referred to as the multipactoring
threshold:

Vo = (2*pi*d/lambda)^2 * (me*c^2)/(pi*e)

where:
Vo is the voltage between the sides of the cavity
me= mass of electron
lambda = wavelength
d = spacing between walls
c = speed of light (3E8 m/sec)
e = charge on an electron

The secondary electron emission actually goes down as the electron energy rises
over the peak, so breakdown can sometimes be avoided by rapidly raising the
RF power (as in a pulsed radar system, for instance).

If the pressure is high, then the electron will likely hit another gas molecule
or atom before hitting the other side, so multipaction is less likely. Therefore,
the mean free path would need to be on the order of the spacing for multipaction
to occur.

Interestingly, aluminum seems to have a really high secondary emission coefficient,
a good reason for plating it with something else in a waveguide intended for
use in vacuum.